Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
826 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 219 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#14579107 | C2 | semidirect |
| 4. #23765669 | C2 | direct (N × H) |
| 5. C2×#19098339 | C2 | semidirect |
| 6. C2×#494×C79 | C2 | semidirect |
| 12. C2×#14579107 | C22 | semidirect |
| 18. #19098339 | C22 | semidirect |
| 23. #494×C79 | C22 | semidirect |
| 132. C2×C79 | #2251 | semidirect |
| 139. C2×#494 | D79 | semidirect |
| 142. C79 | C2×#2251 | semidirect |
| 158. #494 | C2×D79 | semidirect |
| 268. C2 | #23765669 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579107 | 2 |
| C22×#14579104 | 2 |
| C2×#19098947 | 2 |
| #23765669 | 2 |
| C2×#19098339 | 2 |
| C2×#494×C79 | 2 |
| C2×#2251 | 79 |